For the approximation in L_(p)-norm,we determine the weakly asymptotic orders for the simultaneous approximation errors of Sobolev classes by piecewise cubic Hermite interpolation with equidistant knots.For p=1,∞,we ...For the approximation in L_(p)-norm,we determine the weakly asymptotic orders for the simultaneous approximation errors of Sobolev classes by piecewise cubic Hermite interpolation with equidistant knots.For p=1,∞,we obtain its values.By these results we know that for the Sobolev classes,the approximation errors by piecewise cubic Hermite interpolation are weakly equivalent to the corresponding infinite-dimensional Kolmogorov widths.At the same time,the approximation errors of derivatives are weakly equivalent to the corresponding infinite-dimensional Kolmogorov widths.展开更多
基金supported by the National Natural Science Foundations of China(Grant No.11271263).
文摘For the approximation in L_(p)-norm,we determine the weakly asymptotic orders for the simultaneous approximation errors of Sobolev classes by piecewise cubic Hermite interpolation with equidistant knots.For p=1,∞,we obtain its values.By these results we know that for the Sobolev classes,the approximation errors by piecewise cubic Hermite interpolation are weakly equivalent to the corresponding infinite-dimensional Kolmogorov widths.At the same time,the approximation errors of derivatives are weakly equivalent to the corresponding infinite-dimensional Kolmogorov widths.
